We study the charmonium coherent photoproduction and hadroproduction consistently with modifications from both cold and hot nuclear matters. The strong electromagnetic fields from fast moving nucleus interact with the other target nucleus, producing abundant charmonium in the extremely low transverse momentum region pT < 0.1 GeV/c. This results in significative enhancement of J/ψ nuclear modification factor in semi-central and peripheral collisions. In the middle pT region such as pT < 3 ∼ 5 GeV/c, J/ψ final yield is dominated by the combination process of single charm and anti-charm quarks moving in the deconfined matter, c +c → J/ψ + g. In the higher pT region, J/ψ production are mainly from parton initial hard scatterings at the beginning of nucleus-nucleus collisions and decay of B hadrons. We include all of these production mechanisms and explain the experimental data well in different colliding centralities and transverse momentum regions. 12.38.Mh, 24.85.+p With the nuclear collisions at the relativistic heavy ion collisions (RHIC) and the large hadron collider (LHC), there have been a lot of interesting topics about nuclear properties studied in experiments and theories. One of the main goals at RHIC and LHC is to find a deconfined state of nuclear matter, called "quark-gluon plasma" (QGP), which may be produced in the extremely high energy and/or baryon densities with a phase transition [1], and furthermore, extract the transport properties of this QGP [2]. There are also other projects referred to as "non-QGP " physics, concerning about cosmic ray physics and others [3]. As QGP can only be produced in the nucleon collisions in the overlap area of two nuclei, "non-QGP " topics are usually studied in Ultra-peripheral nuclear collisions (UPC) where QGP background is absent.In order to study the existence of the extremely hot deconfined matter, produced in the early stage of heavy ion collisions, J/ψ abnormal suppression has been proposed as one of sensitive signals by Matsui and Satz in 1986 [4]. J/ψ suffers relatively weaker dissociation by the hadron gas compared with QGP, due to its large binding energy [5]. With strong color screening effect and parton inelastic scatterings of QGP, J/ψ production can be significantly suppressed in nucleus-nucleus collisions, which has been observed in many experiments at RHIC and LHC colliding energies in semi-central and central collisions (with impact parameter b < 2R A , where R A is the nuclear radius) [6][7][8][9]. From RHIC to LHC, J/ψ production is relatively enhanced in the transverse momentum region p T ≤ 3 ∼ 5 GeV/c compared with the scale of the pp collisions [8]. This phenomenon has been well explained with charmonium regeneration mechanism: At higher colliding energy, more charm quark pairs can be produced from hard process in hadronic collisions, which enhance the recombination probability of charm and anti-charm quarks inside QGP [10][11][12][13][14]. New J/ψs are continuously regenerated during the QGP evolutions. With sufficiently high initial tem...